Which of the following statements must be true about a rectangle? Choose all answers that apply: Choose all answers that apply: A It has four sides of equal length. B It has four right angles. C It has two pairs of parallel opposite sides.

To solve the inequality |2x-6|<4, we break it down into two inequalities and solve for the range of values. Then, we can plot the solution on a number line.

The given inequality is |2x-6|<4. To solve this inequality, we need to break it down into two separate inequalities:

Solving these inequalities will give us the range of values that satisfy the original inequality. Once we have the solution, we can plot it on a number line.

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Answer:

Step-by-step explanation:

an absolute value has two solutions, one negative and one positive.

so 2x-6<-4

2x<2

x<1

and

2x-6<4

2x<10

x<5

1>x<5

Option A is correct

Answer:

The length of each side of the original square was [tex]15[/tex] inches

Step-by-step explanation:

Let

x------> the length side of the original square

we know that

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the length side of the square

In this problem

[tex]b=(x+2.5)\ in[/tex]

[tex]P=70\ in[/tex]

substitute

[tex]70=4(x+2.5)[/tex]

solve for x

[tex]70=4x+10[/tex]

[tex]4x=70-10[/tex]

[tex]x=60/4=15\ in[/tex]

The distance between the ships is changing at a rate of 39 km/hr at 4:00 PM. This is calculated using differentiation of the Pythagorean theorem relating distances between the ships.

This is a typical

related rates problem

in calculus. Before we start, let's mark the distance between ship A and ship B as C, the distance that A traveled as X (X=35 km/hr*4 hr = 140 km), and the distance B traveled as Y (Y=20 km/hr*4 hr = 80 km). Note that X, Y, and C form a right triangle. By using the Pythagorean theorem, we get C²=X²+Y², which we can differentiate with respect to time (t) to obtain, 2C * dC/dt = 2X * dX/dt + 2Y * dY/dt. As we're solving for dC/dt (rate of change of the distance between the two ships), we get dC/dt = (X * dX/dt + Y * dY/dt) / C. Plugging in the known values (X=140 km, Y=80 km, dX/dt=35 km/hr, dY/dt=20 km/hr, and C=170 km, as it hasn't changed since they started), we get dC/dt = (140*35 + 80*20) / 170 = 39 km/hr. So, the distance between the ships is changing at a rate of 39 km/hr at 4:00 PM.

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Marta's wire is 19.2 cm longer than Tia's wire.

Given:

Tia 's wire is 4m 8 cm ⇒ cut into 10 equal pieces

Marta's wire 540 cm ⇒ cut into 9 equal pieces

Question:

How much longer is one of Marta's wires then one of Tia's?

1. Tia's wire is in m and cm unit, so we can not divide it straightly into its equal pieces. First step, we are going to convert meter (m) to millimeter (mm):

Tia's wire = 4 m 8 cm

[tex]\boxed {1 m = 100 cm }[/tex]

[tex]\boxed {= (4 m \times \frac{100 cm}{ 1 m}) + 8 cm ) } \\\boxed {= 400 cm + 8 cm }\\\boxed {= 408 }[/tex]

2. Second step, calculate each pieces Tia's wire:

She cut this wire into 10 equal pieces:

[tex]\boxed {= \frac{408}{10} } \\\boxed {= 40.8 cm }[/tex]

Each piece of Tia's s ribbon is is 40.8 cm long

3. Third step, we are going to calculate Marta's wire:

She has 540 cm and cut it into 9 equal pieces

[tex]\boxed {= \frac{540 cm}{9} }[/tex]

[tex]\boxed {=60 cm }[/tex]

Each pieces Marta's wire is 60 cm long

4. Last step, find the difference between Tia's wire and Marta's:

[tex]\boxed {=60 cm -40.8 cm }\\\boxed {=19.2 cm }[/tex]

So, Marta's wire is 19.2 cm longer than Tia's wire

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Keywords: converting, conversion, dividing, subtraction, find the difference, converting meter to centimeter, converting unit of length

The thickness of a thin film of diamond can be calculated using the formula t = (m * λ) / (2 * n), where m is the number of fringes, λ is the wavelength of light used, and n is the refractive index of diamond.

The thickness of a thin film of diamond can be determined using the formula:

t = (m * λ) / (2 * n)

where t is the thickness, m is the number of fringes, λ is the wavelength of light used, and n is the refractive index of diamond.

In this case, the number of fringes is given as 14 per centimeter, which can be converted to 140 per meter. The wavelength of the light used is not provided, so we cannot determine the thickness without that information.

Answer:

a = -6

Step-by-step explanation:

Answer:

m = (12 - 7) / (-39 - 26) = 5/(-65) = -1/13

Final answer:

To find the critical value for α = 0.025 in a one-tailed test, we look at the standard normal distribution tables; the critical value is approximately -1.96.

Explanation:

The question pertains to hypothesis testing in the context of proportion analysis. To determine the critical value for a significance level α = 0.025 in a one-tailed test about a proportion, we use the standard normal distribution (Z-distribution). Given that the sample size is large (n=400), it is appropriate to use a Z-test for this calculation. The critical value corresponds to the Z-score that has 0.025 of the distribution's area to its right (since we are checking for 'less than 10% defective').

Referring to standard normal (Z) distribution tables or using statistical software, we can find that the critical value for α = 0.025 for a one-tailed test is approximately -1.96. This is the Z-score such that the area under the normal curve to the right of this value is 0.025. If the calculated Z-score obtained from the sample proportion is less than -1.96, we would reject the null hypothesis that the proportion of defective peaches is less than 10%.

Answer:

B

Step-by-step explanation:

The answer above me ^^

To solve this problem, all we have to do is to use a conversion factor to convert millisecond into seconds. We know that there are 1000 milliseconds in a second, therefore:

pitcher’s arm rotation = 7 degrees / millisecond * (1000 milliseconds / second)

pitcher’s arm rotation = 7,000 degrees / second

Answer:

7000 Hope this helps and if it does remember to give me a like , please and thank you!

There are 3 trumpet players.

We have,

Let's assume the number of trumpet players is represented by "x".

According to the given information, the number of saxophone players is three times the number of trumpet players, so the number of saxophone players would be 3x.

It is also stated that there are 10 less saxophone players than the total number of trumpet and saxophone players.

So, the number of saxophone players would be (x + 3x) - 10, which simplifies to 4x - 10.

Since the number of saxophone players is equal to 4x - 10, we can set up an expression to solve for x:

4x - 10 = x

To isolate x, subtract x from both sides of the expression:

4x - x - 10 = x - x

This simplifies to:

3x - 10 = 0

Next, add 10 to both sides:

3x - 10 + 10 = 0 + 10

This yields:

3x = 10

Finally, divide both sides by 3:

(3x) / 3 = 10 / 3

The solution is:

x = 10/3 or approximately 3.33

Therefore,

There are approximately 3.33 trumpet players.

Since you cannot have a fraction of a player, we can conclude that there are 3 trumpet players.

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An equation is formed when two equal expressions are equated together with the help of an equal sign '='. The solution of the given equation,−2 − (+7) is −9.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Given an equation, −2 − (+7) which is needed to be solved. Therefore, The given equation can be solved as shown below.

−2 − (+7)

Open the brackets,

= −2 − 7

Add the two terms,

= −9

Hence, the solution of the given equation,−2 − (+7) is −9.

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Answer:

1/3

Step-by-step explanation: